reserve M for non empty MetrSpace,
  c,g1,g2 for Element of M;
reserve N for non empty MetrStruct,
  w for Element of N,
  G for Subset-Family of N,
  C for Subset of N;
reserve R for Reflexive non empty MetrStruct;
reserve T for Reflexive symmetric triangle non empty MetrStruct,
  t1 for Element of T,
  Y for Subset-Family of T,
  P for Subset of T;
reserve f for Function,
  n,m,p,n1,n2,k for Nat,
  r,s,L for Real,
  x,y for set;
reserve S1 for sequence of M,
  S2 for sequence of N;

theorem Th11:
  for r being Real holds N is Reflexive & 0<r implies w in Ball(w,r)
proof
  let r be Real;
  assume N is Reflexive;
  then
A1: dist(w,w) = 0 by METRIC_1:1;
  assume 0<r;
  hence thesis by A1,METRIC_1:11;
end;
